1

f[x_]  =  (x  -  alp)^2  +  bet // 
        Expand

2

A  =  {{1, 2}, {2, 3}}
z  =  {x, y}
h  =  {1, -1}

MatrixForm[A]

    MatrixForm[A . z]

    MatrixForm[h]

Solve[A . z  -  h  ==  0]

MatrixForm[Inverse[A]]

Inverse[A]  .  h

3

Integrate[x Exp[-x],  x]

4

<< Calculus`VectorAnalysis`

Clear[x, y, z]
u[x_, y_, z_]  =  {x^2   + z,  y^2   +  z,  
        z^2  +  z}

MatrixForm[u[x, y, z]]

SetCoordinates[Cartesian[x, y, z]]
Div[u[x, y, z]]

Curl[u[x, y, z]]

Laplacian[u[x, y, z]]

6

Series[Sin[x], {x, 0, 3}]

Series[Cos[x], {x, 0, 3}]